To determine which of the given points lie on the line described by the equation [tex]\(y = \frac{1}{2}x\)[/tex], we need to check if each point satisfies this equation.
The points we need to check are:
A. [tex]\((2,1)\)[/tex]
B. [tex]\((-2,-1)\)[/tex]
C. [tex]\((4,2)\)[/tex]
D. [tex]\((-2,1)\)[/tex]
E. [tex]\((3,6)\)[/tex]
F. [tex]\((3,15)\)[/tex]
Let's check each point one by one:
1. Point (2, 1):
- Substitute [tex]\(x = 2\)[/tex] into the equation [tex]\(y = \frac{1}{2}x\)[/tex]:
[tex]\[
y = \frac{1}{2} \times 2 = 1
\][/tex]
- The point [tex]\((2, 1)\)[/tex] satisfies the equation [tex]\(y = \frac{1}{2}x\)[/tex]. So, [tex]\((2, 1)\)[/tex] is on the line.
2. Point (-2, -1):
- Substitute [tex]\(x = -2\)[/tex] into the equation [tex]\(y = \frac{1}{2}x\)[/tex]:
[tex]\[
y = \frac{1}{2} \times -2 = -1
\][/tex]
- The point [tex]\((-2, -1)\)[/tex] satisfies the equation [tex]\(y = \frac{1}{2}x\)[/tex]. So, [tex]\((-2, -1)\)[/tex] is on the line.
3. Point (4, 2):
- Substitute [tex]\(x = 4\)[/tex] into the equation [tex]\(y = \frac{1}{2}x\)[/tex]:
[tex]\[
y = \frac{1}{2} \times 4 = 2
\][/tex]
- The point [tex]\((4, 2)\)[/tex] satisfies the equation [tex]\(y = \frac{1}{2}x\)[/tex]. So, [tex]\((4, 2)\)[/tex] is on the line.
4. Point (-2, 1):
- Substitute [tex]\(x = -2\)[/tex] into the equation [tex]\(y = \frac{1}{2}x\)[/tex]:
[tex]\[
y = \frac{1}{2} \times -2 = -1
\][/tex]
- The point [tex]\((-2, 1)\)[/tex] does not satisfy the equation [tex]\(y = \frac{1}{2}x\)[/tex] because [tex]\(\frac{1}{2} \times -2 = -1\)[/tex], not 1. So, [tex]\((-2, 1)\)[/tex] is not on the line.
5. Point (3, 6):
- Substitute [tex]\(x = 3\)[/tex] into the equation [tex]\(y = \frac{1}{2}x\)[/tex]:
[tex]\[
y = \frac{1}{2} \times 3 = 1.5
\][/tex]
- The point [tex]\((3, 6)\)[/tex] does not satisfy the equation [tex]\(y = \frac{1}{2}x\)[/tex] because [tex]\(\frac{1}{2} \times 3 = 1.5\)[/tex], not 6. So, [tex]\((3, 6)\)[/tex] is not on the line.
6. Point (3, 15):
- Substitute [tex]\(x = 3\)[/tex] into the equation [tex]\(y = \frac{1}{2}x\)[/tex]:
[tex]\[
y = \frac{1}{2} \times 3 = 1.5
\][/tex]
- The point [tex]\((3, 15)\)[/tex] does not satisfy the equation [tex]\(y = \frac{1}{2}x\)[/tex] because [tex]\(\frac{1}{2} \times 3 = 1.5\)[/tex], not 15. So, [tex]\((3, 15)\)[/tex] is not on the line.
Therefore, the points that lie on the line [tex]\(y = \frac{1}{2}x\)[/tex] are:
- [tex]\((2, 1)\)[/tex]
- [tex]\((-2, -1)\)[/tex]
- [tex]\((4, 2)\)[/tex]
